My mom is undergoing chemo - but she won't wash her hands!
This can be so frustrating, but hang in there. You need to understand why she is not doing that. My guess is that extra step takes energy out of her that she may not want to use. It's an effort to go into another room, partially undress, bend, redress, balance, and walk back to where she was before. She may be very concerned about her balance, nausea, and dizziness, too -- holding onto the sink may be more important than using it!
It could also be a small semblance of her maintaining control, choosing not to do something because she can. Cancer makes people feel helpless oftentimes, and they may act out to just feel like they have some power.
Consider some other creative solutions. Would she use a walker? Would she use sanitary wipes for babies? Maybe the soaps dry her skin and you could find an antibacterial lotion that smells great.
Bottom line, though, her body is already dealing with the germs within. It's more important to have her use the sanitizers in public than in your home, where you are probably all much more conscious than outside the home. Also, you can help by periodically taking turns in cleaning the bathroom. Good luck.